ks (version 1.6.13)

Hbcv, Hbcv.diag: Biased cross-validation (BCV) bandwidth matrix selector for bivariate data

Description

BCV bandwidth matrix for bivariate data.

Usage

Hbcv(x, whichbcv=1, Hstart, kfold=1)
Hbcv.diag(x, whichbcv=1, Hstart, kfold=1)

Arguments

x

matrix of data values

whichbcv

1 = BCV1, 2 = BCV2. See details below

Hstart

initial bandwidth matrix, used in numerical optimisation

kfold

value for k-fold bandwidth selection. See details below

Value

• BCV bandwidth matrix.

Details

Use Hbcv for full bandwidth matrices and Hbcv.diag for diagonal bandwidth matrices. These selectors are only available for bivariate data.

There are two types of BCV criteria considered here. They are known as BCV1 and BCV2, from Sain, Baggerly & Scott (1994) and they only differ slightly. These BCV surfaces can have multiple minima and so it can be quite difficult to locate the most appropriate minimum.

If Hstart is not given then it defaults to k*var(x) where k = $\left[\frac{4}{n(d+2)}\right]^{2/(d+4)}$, n = sample size, d = dimension of data.

For large samples, k-fold bandwidth selection can significantly reduce computation time. The full data sample is partitioned into k sub-samples and a bandwidth matrix is computed for each of these sub-samples. The bandwidths are averaged and re-weighted to serve as a proxy for the full sample selector.

References

Sain, S.R, Baggerly, K.A. & Scott, D.W. (1994) Cross-validation of multivariate densities. Journal of the American Statistical Association. 82, 1131-1146. Duong, T. & Hazelton, M.L. (2005) Cross-validation bandwidth matrices for multivariate kernel density estimation. Scandinavian Journal of Statistics. 32, 485-506.

See Also

Hlscv, Hscv

Examples

data(unicef)
Hbcv(unicef)
Hbcv.diag(unicef)